Some "vintage" bits of equipment moght be good choices for some people, but in general this is not the case. IMO only people experienced with the technical issues of older equipment should go in that direction.

Older turntables are usually badly worn in their mechanical parts and need extensive (and expensive) restoration to perform worth a damn, and the same may also be true of amplifiers and receivers.

Speakers have NOTHING to do with analog or digital, since they are always driven by an ANALOG output from an amplifier. Speakers are electromechanical transducers (analog by definition).

It would be helpful to know what you expect your system to be and do, functionally speaking.

I would recommend that you start with a quality AVR, such as the Cambridge 551R, and some good speakers from PSB or KEF or Monitor Audio, and go from there. All other equipment will be well-served by using these as the heart of your system.

Specific recommendations would depend on your budget, which you need to specify in detail. A good receiver and 5 speakers can be had for around $2500-3000. 

Cheap systems can be thrown together for half of that, or less, with a significant lessening of sound quality. 

I see no conflict in integrating varied equipment.  In the broad view, all systems are varied in age and technology anyway.  If you buy everything on X date, whether that is today or years ago, you will still be able to connect stuff to it in the future.

As commysman said, all speakers are suitable and all are driven by analog signals, in the end.  That's mostly true of amps, also. 

There are plenty of systems that integrate digital and/or video together with vintage (or current) stereo equipment.  Details later, if I can, but be of good cheer, of course it can be done.

The best suggestion/advice I or any else can give you is to make the effort and go out and audition some gear, especially speakers. If you have to drive an hour or so, so be it. You will be amply rewarded by ending up with a system that you will be satisfied with. Your other option is to listen to a bunch of recommendations by people espousing their personal favorite choices in gear and speakers. Relying on someone else's recommendation for speakers is akin to having someone else choose a mail order bride for you. The chances of getting something you like and can live with are slim to none.

FWIW: I have one system in a dedicated room that serves for music and video. It includes tube amplifiers, solid state amplifiers, a hybrid preamp, solid state surround processor, two pair of electrostatic speakers, four sub woofers, belt drive TT, cassette tape deck, CD/DVD/BluRay players, etc. and is fully integrated with a 50" LCD and computer music server. Some of it is vintage (rebuilt tube amps from the 70's), some of it is new (BluRay player, sub woofer amplifiers, computer music server) and some of it is DIY (two sub woofers). The rest is a mixture of products from several eras.

With that said, what's your budget?

1) The Audio-Technica LP60 turntable ($99 from Needle Doctor). This comes complete with cartridge and is plug-and play. The next step up in quality would be the the Pro-Ject Essential for $299.

2) Harman-Kardon 3490 receiver (includes phono preamp) (Around $300).

3) Pioneer BS-41 speakers ($140 from Amazon)

The 3490 receiver has plenty of amplifier power to drive virtually any speakers (120W per channel), a built-in phono preamp, a DAC (digital inputs provided), and an FM tuner section. The sound quality is exceptionally good for its price, and the features are excellent. This is the perfect unit to build a system around. You can add much better speakers, turntable, etc. as time goes by and this unit will have the quality to work well with them.

The Pioneer BS-41 speakers are also exceptionally good for their price. The next step up in sound quality would be to go to the Wharfedale Diamond 10.1 speakers, which are $350 per pair.

The HK 3490 has 120 watts per channel, which is enough to drive 98% percent of the speakers on the planet very very well.

There is absolutely no need for an external amplifier.

If $300 is your price limit, the Pro-Ject Essential is $299 now at Needle Doctor, and that would be my recommendation. Buying a turntable used could get you something that has problems, and I personally would recommend buying only a new unit.

I do a lot of both 2 channel stereo and I also have a surround setup. In my opinion its not about Analog vs Digital its about 2 channel vs multichannel. You will not get the absolute best sound out of a CD player for example running it through a surround receiver. A receiver has so much going on circuitry wise: power amp, preamp, HDMI switching, Digital Processing, etc. There are so many opportunities for distortion to sneak into the signal, not to mention the use of lower quality parts to keep the price down. Receivers can make a CD sound a little different on a surround system with some neat processing but purists will say that you are not experiencing the music as it was intended. On a straight 2 channel system you can arguably achieve a more accurate representation of how the material sounded on the monitors in the studio during the recording and mastering.

First you have to decide on your sources. If you want to do surround sound you will need to go with a modern receiver. If you want to listen to CD's you can always just throw them in a Blu Ray or DVD player. Cassette tapes are pretty much obsolete and the receiver will have a tuner built in. A turntable is probably the only analog component that you would need to integrate into the system unless you have some nostalgia for an old reel to reel or something.

If you only want to listen to music I would recommend a basic 2 channel system. Perhaps starting with a Tuner/Pre and a decent amp or an integrated amp and some sources. Just a thought if you are considering 2 channel: A company called Sonos makes an excellent product for bringing your 2 channel into 2014 source wise. The Sonos Connect is basically an online media streamer with analog and digital outputs.  For $350 its kind of pricey for starting out but I wanted to mention it as this thing goes both ways. I think its easier to integrate new digital devices with high quality 2 channel separate systems.

That being said I have a few suggestions to help you keep you system open for future upgrades. I am assuming that you will be going the surround route...

First, if you can find a receiver that has an entire preout section you can basically bypass the power amp section of the receiver and use it as a gloried preamp, sending line level signals to an external 5 channel power amp. In my experience whenever a power amp is added to a lower end receiver the sound of the system will be greatly improved. I had the center channel amp poop out on my Yamaha RXV-663. I was going to toss it but saw that it had preouts for all channels. I picked up a vintage NAD 906 multi channel power amp and rescued the system while greatly improving the sound.

You can also use this trick to optimize your system for CDs, radio, and Vinyl. Although Analog/Digital has nothing to do with speakers, some speakers are great for surround setups but suck for music. Using the preout section of the receiver you can send a signal to a 2 channel power amp and power a pair of cheap but musical speakers like early Polk Monitor Series. Depending on the receiver you could leave them on for watching movies too but I would not recommend it. Another thing you can do is just hook up a pair of vintage speakers up to the speaker B section of a receiver and switch them on for music and off for surround and basically run two systems to get the best of both worlds.

Another thing I like about my little Yamaha is its pure direct feature which claims to shutoff all unnecessary circuitry when listening to analog sources.

I am on a bit of a ramble now so want to outline a quick starter system. I would recommend buying a brand new receiver but you can probably pick up almost everything else used and have no issues...

5.1 AV Receiver W/ AB speaker outputs and a phono input. (Full preamp section is a bonus for future expansion and a failsafe if any part of the amplifier section fails) - OOPS also make sure it has Dolby TrueHD and DTS HD Master decoders.

Blu Ray player with Apps for -Blu Ray, DVD, CD, Pandora, Netflix etc

Decent set of surround speakers. I use a Klipsch Synergy Set, boston and polk make decent starter sets as well and a lot of them come with a 8, 10, or 12" powered sub which is great for movies.

The above is all you will need to get started. From there if you want something a little better for music you can upgrade your front stage to full range floor standers or try the vintage speakers on the B output of the receiver option. If you want a better CD player you can pick one up and plug it right in. If you want to try crazy stuff later you can try a surround or 2 channel power amp but in many cases stepping up to a more expensive receiver is a better choice.

If you only want music its time to hit the thrifts and pawn shops for your first vintage 2 channel system!

I jumped the gun and did not see that you had already started picking components. If you are going with 2 channel I would recommend looking into a used integrated amp from NAD or Adcom to start out. A lot of stereo shops and even some pawn shops will give you a couple weeks to return them if they malfunction. IMO you get more bang for your buck with used gear if you can handle the risk.